July 24, 2006

Exhibit (d)(3)

July 24, 2006

Hercules Holding II, LLC

c/o Bain Capital Partners, LLC
000 Xxxxxxxxxx Xxxxxx
Xxxxxx, XX 00000

c/o Kohlberg Kravis Xxxxxxx & Co. L.P.
0000 Xxxx Xxxx Xxxx, Xxxxx 000
Xxxxx Xxxx, XX 00000

c/x Xxxxxxx Xxxxx Global Private Equity
Four World Financial Center
Floor 00
Xxx Xxxx, XX 00000

Dear Sirs:

This letter relates to the Agreement and Plan of Merger by and among HCA Inc., Hercules Holding II, LLC and Hercules Acquisition Corporation, dated July 24, 2006 (the “Merger Agreement”).

In connection with the proposed acquisition of HCA Inc. (the “Company”) contemplated by the Merger Agreement, I am pleased to confirm my agreement to: (1) invest in the Company, as it shall exist immediately after the completion of the Merger as contemplated by the Merger Agreement, on such material terms as are set forth in the Summary of Management Equity Summary of Terms and the Appendices attached thereto (the “Summary”) attached to this letter; and (2) execute certain definitive agreements (including those agreements regarding the grant of New Options (as such term is defined in the Summary), the material terms of which are set forth in the Summary (the “Management Agreements”).

My agreement described above is subject to and conditioned upon the occurrence of the Merger and the negotiation and agreement to mutually satisfactory definitive versions of the Management Agreements. You and I agree that such agreements will be negotiated in good faith and reasonably promptly after the execution of the Merger Agreement.

If the Merger Agreement terminates for any reason before the Merger occurs, this letter agreement will also terminate and have no more force and effect on either of us.

You and I acknowledge that nothing in this letter creates an exclusive arrangement between us and no binding agreement shall become effective until immediately prior to the closing of the Merger.

Sincerely,

/s/ Xxxx X. Xxxxxxxx, Xx.
Xxxx X. Xxxxxxxx, Xx.

[Signature Page of Management Investment Letter]

Accepted and agreed this 24th day of July, 2006 by:

Hercules Holding II, LLC

	By:	/s/ Xxxxx Xxxxxx
		Name:	Xxxxx Xxxxxx
		Its: President and Assistant Secretary